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Master's Dissertation
DOI
Document
Author
Full name
Luiz Felipe Villar Fushimi
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Lymberopoulos, Alexandre (President)
Lodovici, Sinuê Dayan Barbero
Silva, Márcio Fabiano da
Title in Portuguese
Representações integrais de soluções do problema de Björling de tipo tempo em R^4
Keywords in Portuguese
Números paracomplexos
Problema de Björling
Representação de Weierstrass
Superfícies mínimas
Abstract in Portuguese
Nesta dissertação, estudamos o problema de Björling para superfícies de tipo tempo nos espaços de métrica indefinida R^4_1 e R^4_2. Após apresentar uma versão paracomplexa do teorema de representação de Weierstrass para superfícies mínimas de tipo tempo, utilizamos esse teorema para obter uma fórmula de representação para as soluções desse problema de Björling, e através de extensões paraholomorfas dos dados iniciais do problema mostramos que a solução dada por essa fórmula é localmente única. Em seguida, apresentamos duas possíveis maneiras de se obter simetrias para soluções desse problema de Björling: através de uma versão paracomplexa do princípio de reflexão de Schwarz, e através de reflexões ao longo de k-planos que intersectam ortogonalmente a superfície.
Title in English
Integral representations for solutions to timelike Björling problems in R^4
Keywords in English
Björling problem
Minimal surfaces
Split-complex numbers
Weierstrass representation
Abstract in English
In this dissertation, we study the Björling problem for timelike surfaces in the spaces of indefinite metric R^4_1 and R^4_2. After presenting a split-complex version of the Weierstrass representation theorem for minimal timelike surfaces, we use this theorem to obtain a representation formula for the solutions of this Björling problem, and through split-holomorphic extensions of the problems initial data we show that the solution given by this formula is locally unique. Following this, we present two possible methods through which symmetries for the solutions of this Björling problem may be obtained: through a split-complex version of the Schwarz reflection principle, and through reflections alongside k-planes that intersect the surface orthogonally.
 
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diss_corr_LuizFelipe.pdf (442.69 Kbytes)
Publishing Date
2019-05-07
 
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